This open access textbook fills a gap in that it introduces readers to the theory and
applications of the Phase-Field technique. Phase Field over the years has emerged as a
standard tool for materials research just as the Finite-Element technique has in structure
mechanics. Whereas the few existing textbooks on this topic are intended for advanced readers
this one is made accessible to the widest possible audience through an engaging lecture
format. The content grows out of a course the authors teach for graduate students at
Ruhr-University Bochum. Even readers who may at first have no clue at all what a Phase Field
is and for what it is used are invited on a journey from general physics of thermodynamics and
wave mechanics through applications in all fields of materials science up to the central
questions of physical being. On this journey all the necessary techniques are detailed mostly
formulated in a mathematical language easily understood by engineers and natural scientists.
